Inspired by [1]}, we employ DAGNN to encode the job
DAGs information in a set of embeddings, which contain per-node embedding
\(\mathbf {e}_{v}^{i}\)  and per-job embedding \(\mathbf {y}^{i}\) . The
former captures information about the node and its predecessor nodes
and the latter aggregates information across the set of nodes without
successors \(\mathcal {T}\) . Given the feature vectors \(\mathbf {x}_{v}^{i}\) 
of node \(v\)  in job DAG \(G_{i}\) , we build a per-node embedding \(\left(G_{i},\mathbf {x}_{v}^{i}\right)\longmapsto \mathbf {e}_{v}^{i}\) ,
and compute a per-job embedding for each DAG \(G_{i}\) , \(\left\lbrace  \left(\mathbf {x}_{v}^{i},\mathbf {e}_{v}^{i}\right),v\in \mathcal {T}_{i}\right\rbrace  \longmapsto \mathbf {y}^{i}.\) 
Table REF  defines our notation. However, DAGNN is
still computationally expensive since it uses an iterative message
passing scheme. Hence, we propose a novel Pipelined-DAGNN that can
effectively speed up the feature extraction process of DAGNN.
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